1. Field of the Invention
The present invention relates to a method and apparatus for manifesting a characteristic or regularity which is latent and can not be recognized, although such characteristic or regularity actually exists in a complicated symbolic sequence, for example, a nucleotide sequence of DNA, an amino acid sequence of protein, or a digital sequence of decimal expansion of an irrational number and the like. In these sequences, regularity can not be recognized at a glance even when the regularity is included. The present invention enables recognition of characteristic a or regularity included in the symbolic sequence but not yet unrecognized.
2. Description of the Related Art
Some complicated symbolic sequences contain characteristic which has not been recognized by human beings, although the characteristic actually exists. For example, genetic information is specified by a symbolic sequence of long string. The symbols consist of four symbols each indicating one of four kinds of nucleotides. A large number of symbols are one-dimensionally aligned. In the study of genetic information, it is extremely important to recognize a certain regularity hidden in the symbolic sequence indicating genetic information. Besides, if a certain regularity is found in an irrational number, the number xcfx80, and the base of natural logarithm (e), the study of random numbers is intensified and various developments are expected in mathematics.
For such a purpose, various trials have been made for analyzing a symbolic sequence based on a variety of mathematical methods such as the Fourier analysis. However, these trials have not necessarily accomplished successful results. One problem with the conventional analysis methods is that even if a certain regularity is included in a part of a very long symbolic sequence, the latent regularity is buried within the whole sequence and can not be recognized when the whole symbolic sequence is analyzed. Since there is no effective technology to determine in advance in which part of the sequence the regularity exists, there are many characteristics or regularity which can not be recognized by the conventional analysis methods.
An object of the present invention is to provide a method and apparatus which manifests a characteristic or regularity even if such characteristic or regularity exists only in a part of the whole symbolic sequence, and thereby enables recognition of a characteristic or regularity which has not been recognized until now.
Another object of the present invention is to manifest a characteristic or regularity existing throughout the entire sequence.
In one embodiment of the present invention, when a symbolic sequence Ij (j=1xcx9cm) is given, there is an effected conversion to a parallel sequence A(k) of partial symbolic sequences in which the suffix j is aligned in the following positional relation:
j=1, 2, . . . kxe2x88x921, k
j=k+1, k+2, . . . k+kxe2x88x921, k+k
:
:
:
j=(nxe2x88x921)k+1, (nxe2x88x921)k+2, . . . (nxe2x88x921)k+kxe2x88x921, (nxe2x88x921)k+k
j=nk+1, nk+2, . . . nk+kxe2x88x921, nk+k.
In the alternative, the positional relation may be the following:
j=1, 2, . . . kxe2x88x921, k
j=k+k, k+kxe2x88x921, . . . k+2, k+1
:
:
:
j=(nxe2x88x921)k+k, (nxe2x88x921)k+kxe2x88x921, . . . (nxe2x88x921)k+2, (nxe2x88x921)k+1
j=nk+1, nk+2, . . . nk+kxe2x88x921, nk+k.
Herein, k represents an integer of 2 or more, n represents an integer such that nk less than mxe2x89xa6nk+k, and when the suffix j is m+1 or more, the processing is ignored.
Then, the converted parallel sequence A(k) is output using one or more expression means selected from hue, lightness and saturation of color and from interval, tone and volume of sound.
Equidistant Letter Sequences in the Book of Genesis (Doron Witztum, Eliyahu Rips and Yoav Rosenberg, Statistical Science 1994, Vol. 9, No. 3, page 429-438) introduces a technology in which a code hidden in a one-dimensional letter sequence is decoded by converting the one-dimensional letter sequence to a parallel sequence A(k) of partial symbolic sequences. In this technology, there is required an operation to extract letters having senses from the parallel sequence A(k) of partial symbolic sequences, and it can not be used for other sequences than the letter sequence. Further, when a certain regularity is to be recognized in a symbolic sequence which is irregular at a glance and which is often found in a natural field, inconsistency, namely, regularity can not be recognized unless the regularity to be recognized has been recognized in advance, can not be solved.
In the present invention described above, since a parallel sequence A(k) of partial symbolic sequences is output using one or more expression means selected from hue, lightness and saturation of color and from interval, tone and volume of sound, even if regularity is not known in advance, that regularity is manifested by a pattern of hue, lightness and saturation of color and interval, tone and volume of sound and can be easily recognized.
In another embodiment of the present invention, when a one-dimensional symbolic sequence Ij (j=1xcx9cm) is given, there is an effected conversion to a parallel sequence A(k) of partial symbolic sequences in which the suffix j is aligned in the following positional relation:
j=1, 2, . . . kxe2x88x921, k
j=k+1, k+2, . . . k+kxe2x88x921, k+k
:
:
:
j=(nxe2x88x921)k+1, (nxe2x88x921)k+2, . . . (nxe2x88x921)k+kxe2x88x921, (nxe2x88x921)k+k
j=nk+1, nk+2, . . . nk+kxe2x88x921, nk+k.
In the alternative, the positional relation may be the following:
j=1, 2, . . . kxe2x88x921, k
j=k+k, k+kxe2x88x921, . . . k+2, k+1
:
:
:
j=(nxe2x88x921)k+k, (nxe2x88x921)k+kxe2x88x921, . . . (nxe2x88x921)k+2, (nxe2x88x921)k+1
j=nk+1, nk+2, . . . nk+kxe2x88x921, nk+k.
Further, when p represents a natural number from 2 to less than m, r represents any natural number, the above-described conversion is repeated with changing k to p, p+r, p+2r, p+3r, . . . to obtain parallel sequences of partial symbolic sequences: A(p), A(p+r), A(p+2r), A(p+3r) . . . . Then, the resulted parallel sequences: A(p), A(p+r), A(p+2r), A(p+3r) . . . are further parallel-positioned to make a whole parallel sequences xcexa3A(k). Then, the obtained whole parallel sequences xcexa3A(k) is output. Here, n represents an integer such that nk less than mxe2x89xa6nk+k, and when the suffix j is m+1 or more, the processing is ignored.
In this case, a parallel sequence made by parallel-positioning of p partial symbolic sequences, a parallel sequence made by parallel-positioning of p+r partial symbolic sequences, and parallel sequences made by parallel-positioning of likewise increased number of partial symbolic sequences, are all parallel-positioned. In this processing, if regularity of period length xcex1 is hidden in the symbolic sequence, such regularity is remarkably manifested in a parallel sequence A(xcex1) made by parallel-positioning of partial symbolic sequences of a number of xcex1.
If xcex1 is included in between p, p+r, p+2r, p+3r, . . . rows, regularity of period length xcex1 a is manifested in a parallel sequence of partial symbolic sequences of an analogous number to xcex1. Therefore, increment r regarding the number of the partial symbolic sequences is not necessarily required to be one, and it may advantageously be any natural number. In this case, when the increment r is smaller, the characteristic is more easily manifested.
In this embodiment, regularity of an unknown period length is manifested in a parallel sequence of partial symbolic sequences of some number, and recognition of the characteristic becomes easy.
In the above-described method, it is preferable that each symbol is expressed by a combination of hue, lightness and saturation of color. By this embodiment, as a result of the manifestation of the characteristic hidden in the symbolic sequence through visual means, a more complete understanding regarding the characteristic hidden in the symbolic sequence is possible, and various applications and developments utilizing the characteristic are made possible. Further, the resulting visual pattern is a pattern including mixed regularity and irregularity mixed which has not previously existed, and a visual pattern of which design itself has utility application can be designed.
Each symbol may be expressed by a combination of interval, tone and volume of sound. By expressing the parallel sequence by a combination of interval, tone and volume of sound, a unique audio pattern is created and the characteristic of the symbolic sequence can be recognized through auditory means.
When one symbol is taken out from an original symbolic sequence at an interval of kxe2x88x921 (namely, at every k) to make a symbolic sequence and the method is applied to this extracted symbolic sequence, if regularity of period length k is hidden in the original symbolic sequence, the regularity is manifested and appears remarkably.
When one symbol is taken out from an original symbolic sequence at an interval of kqxe2x88x921 (namely, at every kq) to make a symbolic sequence and the method is applied to this extracted symbolic sequence, if regularity of period length kq is hidden in the original symbolic sequence, the regularity is manifested and appears remarkably.
Further, when any of the above-described methods are conducted with changing k to p, p+r, p+2r . . . , there is formed a whole parallel sequences xcexa3A(k) of a parallel sequence A(p) made by parallel-positioning of p partial symbolic sequences, a parallel sequence A(p+r) made by parallel-positioning of p+r partial symbolic sequences, and parallel sequences made by parallel-positioning of likewise increased number of partial symbolic sequences, and regularity of period length xcex1 appears remarkably in a parallel sequence A(xcex1) formed by parallel-positioning of k (=xcex1) partial symbolic sequences. Therefore, characteristic or regularity of unknown period length is manifested, and recognition of characteristic or regularity becomes easy.
According to this method, even if the period length xcex1 of regularity or characteristic is included between p, p+r, p+2r, . . . rows, characteristic or regularity is manifested in a parallel sequence formed by parallel-positioning partial sequences of a number approximated to xcex1, and increment r is not necessarily required to be one. It becomes possible to manifest the characteristic using a small amount of data processing, by selecting increment r which has been adjusted to the situation.
Further, by outputting analyzed results by color and/or sound, expressions suitable to situation and observer become possible, and the characteristic is more easily recognizable. The resulting color and/or sound pattern will be an interesting pattern in which regularity and irregularity are mixed, and the method can be utilized also as a designing method.
Especially when an initiation position of regularity is situated at an analysis initiation position, the pattern of having a parabolic shape clearly appears, and regularity of a long period length is manifested clearly, in the whole parallel sequences xcexa3A(k).
The present invention will be recognized more successfully by reading the descriptions of the following examples with the referring drawings.